What are the differences between "play" when referenced by Crumbling Sands, and by Kennen Legend?

Short answer: they're two different meanings of "play" — Kennen's is a trigger that needs resolution; Crumbling Sands' is a conditional check that only needs finalization.

Kennen's Heart of the Tempest ("When you play a card from anywhere other than your hand, empower me") is a triggered ability. Per Rule 419.4.a, the trigger only fires when the act of playing is completed by the card resolving — so if that card is countered or otherwise never resolves, Kennen does not empower.

Crumbling Sands ("Counter a spell if an opponent has played another spell this turn") is a non-triggered conditional check. Per Rule 419.4.b, those checks reference whether the spell was Finalized — meaning it went through finalization and became a Finalized Chain Item. Whether it resolved or was countered afterward doesn't matter.

Concrete difference: opponent plays a spell, you Defy it — Kennen gets no empower, but the spell still counts as "played" for Crumbling Sands. So if they play a second spell, Crumbling Sands can counter it. One catch: "another" excludes the spell Crumbling Sands itself targets, so you can't use it on the opponent's first spell of the turn. (Rule 419.4)